Cooling of the oceanic lithosphere—evidence from geoid anomalies across the Udintsev and Eltanin fracture zones

Earth and Planetary Science Letters, 88 (1988) 289-307 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

289

[5]

Cooling of the oceanic lithosphere--evidence from geoid anomalies across the Udintsev and Eltanin fracture zones M.L. Driscoll 1,, and Barry Parsons

2,..

1 M I T / W H O I Joint Program in Oceanography, Massachusetts Institute of Technology, Cambridge, MA 02139 ( U.S.A.) 2 Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139 (U.S.A.) Received February 6, 1987; revised version received January 27, 1988 The often step-like variation in the marine geoid across fracture zones is believed to reflect the change in age of the ocean floor, and hence in temperature structure of the plate across the fracture zone. The rate of change of the geoid with age has been estimated as a function of age from geoid offsets across fracture zones and used to constrain thermal models of lithospheric cooling. Results from three studies of the geoid offsets across the Mendocino fracture zone are consistent with a thermal plate coofing model having a plate thickness between 100 and 125 km. This is in contrast to results obtained from the combined measurements from fracture zones in the South Pacific, which are not consistent with either the plate model or boundary layer model of cooling. To examine this inconsistency we have measured geoid offsets on Seasat profiles across the Udintsev and Eltanin fracture zones in the South Pacific and tested the robustness of the measurement technique. We used a second-order polynomial that included a step function centered on the fracture zone to estimate the regional geoid and the geoid offset. The polynomials were fit to the geoid profiles using least-squares minimization criteria. Data within a certain distance of the fracture zone were excluded from the fitting procedure in order to minimize the effects of horizontal cooling and lithospheric deformation near the fracture zone. We find that the estimate of the geoid offset is very sensitive to the length of data excluded and that generally, an exclusion width of 100-200 km is needed to avoid anomalies (unrelated to the regional geoid offset) near the fracture zone. Exclusion widths of less than 100 km generally lead to unpredictable errors in the geoid offset estimates. Using exclusion widths of between 150 and 200 km on most profiles, we constructed geoid slope (geoid offset divided by the age offset) versus average age plots for each of the limbs of the two fracture zones. Similar trends were found on both the east and west limbs of the Eltanin and the east limb of the Udintsev. The trends were inconsistent with a single thermal plate thickness and instead showed an initial decrease in slope between 0 and 35 m.y., followed by an abrupt increase followed again by a decrease in slope. In contrast, the west branch of the Udintsev shows an increase in geoid slope values between 20 and 35 m.y., followed by a decrease. The difference in observed trends across the western limb of the Udintsev may be due to the effects of the Louisville Ridge (north of the fracture zone) on the regional geoid. The similarity in trends on the remaining three limbs argues against the effects of isolated thermal or bathymetric anomalies and appears instead, to reflect a general feature of the geoid-slope versus average age relationship across fracture zones. Although the thermal plate coohng model is successful in predicting both seafloor depths and heat flow values out to ages of at least 80 m.y.B.P., it cannot explain the observed geoid slope values for these two fracture zones. It is not clear at this point whether this is due to inadequacies in the cooling model or to peculiarities in fracture zone evolution, possibly caused by small-scale convection driven by the horizontal temperature gradients beneath fracture zones.

1. Introduction

cools and contracts and the depth to the seafloor increases. Empirical depth versus age curves have

A s o c e a n i c l i t h o s p h e r e is c r e a t e d a n d t r a n s p o r t e d a w a y f r o m m i d - o c e a n s p r e a d i n g r i d g e s it

b e e n c o m p i l e d f o r t h e m a j o r o c e a n b a s i n s [1,2] and, in general, show mean seafloor depths increasing as the square root of age out to 60-80 m.y.B.P. At older ages, the seafloor asymptotically approaches a constant depth. Several thermal cooling models have been proposed in order to explain the observed depth versus age relations. In

* Now at: The Analytic Sciences Corporation, 55 Walkers Brook Drive, Reading, MA, 01867, U.S.A. ** Now at: Department of Earth Sciences, University of Oxford, Parks Road, Oxford OX1 3PR, U.K. 0012-821X/88/$03.50

© 1988 Elsevier Science Publishers B.V.

290

the simplest case heat is lost through vertical heat conduction with no limit on the depth to which cooling can occur. This model accurately describes the subsidence of the oceanic lithosphere up to ages between 60 and 80 m.y.B.P, but does not predict the flattening of the mean depth versus age curves for older seafloor. Alternatively, cooling of a finite thickness plate with a bottom surface held at a constant temperature accurately predicts seafloor depths for both young and old ages when the thickness of the plate and the bottom boundary temperature are suitably adjusted. In this model, the heat lost through the upper surface of the plate balances the heat flux from the bottom surface which results in the observed flattening of seafloor depths at large ages. Although the plate cooling model provides an accurate mathematical description of the observed seafloor depths, the model does not specify how the isothermal condition required at the base of the plate can be maintained within the earth. One physical mechanism which has been proposed to bring heat to the base of the plate is small-scale convection [3]. This convection would occur on scales much smaller than the plates themselves and would advect hot material from within the mantle up to the base of the cooling lithosphere. More recently, variations in the height of the marine geoid with seafloor age have been used to constrain thermal cooling models. The isostatic geoid anomaly due to the cooling of the lithosphere is more sensitive than the subsidence of the seafloor to temperature variations at larger depths. This difference is reflected in the weighting by z that appears in the integral equation for the isostatic geoid anomaly but not in the equation for seafloor subsidence:

W(t)

lOmOt (Pm--~?w)

N(t)

-27rGOmfod~z(1-a[T(t, g

fod~{Tm--T(t, Z)) dz z ) -- Tm] }

(1) dz

(2) where w(t) is the variation in seafloor depth with age, N(t) is the variation in geoid height with age and d c is the compensation depth (the remaining parameters are defined in Table 1). The temperature structure T(t, z) is dependent on the assumed cooling model. Unlike seafloor depths, the

TABLE 1 Parameters used in the calculations Parameter

Definition

Value

a

3.1 × 10-5 K - 1

g G

volume coefficient of thermal expansion mean acceleration of gravity gravitational constant

Pm Pw Tm

thermal diffusivity mantle density seawater density mantle temperature

9.82 m s - 2 6.67 x 10-11 m 3 kg-a s-2 8.0 × 10 -v m 2 s - l 3330 kg m - 3 1025 kg m - 3 1365 ° C

geoid contains large amplitude anomalies which are caused by lateral density variations within the mantle. Separating these large-amplitude, longwavelength anomalies from those arising from density and temperature variations within the lithosphere is difficult. Because of this, it is impossible, in most cases, to directly measure geoid height variations as a function of sea floor age. One exception is at oceanic fracture zones where there is an abrupt change in the age of the seafloor across the fracture zone and a corresponding change in the height of the geoid. This offset in the geoid occurs over a distance of several hundred kilometers. A long-wavelength geoid can be subtracted from the observed profile and the remaining geoid offset measured as a function of the age difference across the fracture zone. We assume that the long-wavelength geoid which is removed adequately approximates the regional geoid field, although in our analysis we find that this may not always be true. Geoid slopes (geoid offsets divided by the age offset) estimated across the Mendocino fracture zone show a decrease with increasing age of the seafloor. The measurements are compatible with the plate cooling model assuming a plate thickness of 100-120 km [4,5]. These plate thicknesses agree with those found by modeling the subsidence of the seafloor in the North Pacific [1]. However, offsets across the Udintsev fracture zone in the South Pacific [6] are more consistent with a thermal plate thickness of 50-70 km for ages less than 30 m.y. and a larger plate thickness in the range of 70-90 km for older ages. Subsequent analyses [7,8] also found that distinct thermal plate thick-

291 nesses for ages less than 30 m.y. and greater than 30 m.y. are representative of the South Pacific Ocean. This unexpected finding and the large discrepancy in the estimates of thermal plate thickness between the Mendocino and Udintsev fracture zones cannot be explained by either the half-space or the plate cooling models. In this paper we analyze Seasat profiles across the previously studied Eltanin and Udintsev fracture zones for two main purposes. The first is to test the accuracy of the measurement technique used here to determine the geoid offsets across the fracture zones. The geoid profiles are approximated by a second-order polynomial which includes a step function, and both the length of the profile and the amount of data excluded near the fracture zone are found to greatly affect the determination of the geoid offset. Secondly, each branch of the fracture zones is analyzed separately to see whether observed trends in the geoid slopes are consistent across the whole area and thereby indicative of regional trends, or confined to a particular fracture zone and representative of local thermal or structural anomalies. Both the mea[

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surement technique and data presentation used here are significantly different from those in previous studies [6-8] and roughly twice as m a n y profiles across the Udintsev and Eltanin are used in this analysis than in the previous ones. Despite the differences in method, our results from the Eltanin fracture zone system agree with the previous finding [7,8] that a simple plate cooling model cannot explain the observed geoid offsets. Results from the Udintsev fracture zone were less conclusive and differences were found in the geoid sl0Pe-age relationship between the western and eastern limbs of the fracture zone. However, neither the plate cooling model or half-space cooling model are able to explain the observed geoid slope-age relationships. 2. Udintsev and Eltanin fracture z o n e s

The Udintsev and Eltanin fracture zones in the South Pacific are located on the Pacific-Antarctic Rise which is currently spreading at a full rate of - 6 0 m m / y r (Fig. 1). Seafloor topography is smooth and the spacing between major fracture

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292 zones is fairly large, typical of fast-spreading ridges. Ship-track coverage is sparse but several track lines parallel to the fracture zones provide fairly complete magnetic anomaly identifications sought of the Udintsev fracture zone. Magnetic anomaly locations are taken from Molnar et al. [9]. North of the Udintsev fracture zone the identified anomaly sequence is complete from anomalies 12 to 32. Only one track line contains identifications for anomalies 2 through 6 and these are located north of a presently inactive, small-offset fracture zone between the Udintsev and Eltanin fracture zones. The Eltanin fracture zone system is made up of the closely-spaced Heezen and Tharp fracture zones. North of the Eltanin system anomalies 5 to 18 are located east of the spreading ridge and the sequences 1 to 5c and 18 to 32 to the west. Ages for the magnetic anomalies were determined using the time scale of LaBrecque et al. [10]. The age offset across the Eltanin fracture zone system is 30-34 m.y. at the present and has ranged from 24 to 39 m.y. in the past due to spreading rate variations. At the present time, the Udintsev fracture zone has an age offset of 9-11 m.y. and its age offset has ranged from 7 to 20 m.y. With these large age offsets the amplitudes of the geoid variations across the fracture zones are also quite large (1-5 m at the ridge crest-transform intersections) and distinct in maps of sea-surface heights (e.g. [11]). 3. Method Geoid height offsets were estimated by fitting a second-order polynomial and a step function to the observed profiles. This method was first introduced by Crough [12] to measure offsets on geoid profiles across the Mendocino fracture zone. The second-order polynomial is used to approximate the regional geoid, and the step-function weighted by a value AN approximates the geoid offset at the fracture zone. The total geoid height is given by N ( x ) where: N ( x ) = a + bx + cx 2 + A N . H ( x -

x~)

(3)

where xf = location of fracture zone, and H ( x x r ) = u n i t - s t e p function. Within 100-200 km of the fracture zone, the geoid is affected by lateral diffusion of heat across the fracture zone which

smooths out the sharpness of the geoid offset [4]. Topographic effects created by lithospheric flexure [13] or by the action of bending moments on the free ends of the lithosphere [14] may also be sources of geoid anomalies near the fracture zone. These thermal and mechanical effects are assumed to be localized near the fracture zone and to have little effect on the geoid offset due to the change in lithospheric age outside of this region. In order to avoid biasing the estimate of the regional geoid offset by these unmodeled anomalies, points within a certain distance of the fracture zone were excluded from the fitting process. The width of the zone excluded from the least-squares fitting process substantially alters the geoid step estimation. In this analysis we examined the effects of excluding widths between 0 and 200 km on each side of the fracture zone. Examples from each side of the two fracture zones (Fig. 2) show an increase in the estimated geoid offset with the larger exclusion widths. On the west side of the Udintsev, the geoid offset on profile RO875 increases from 0.73 m when no exclusion width is used, to 1.90 m when a width of 200 km is used. Likewise, the estimated offsets on profile RO185 on the east limb of the Udintsev increases from 0.65 to 2.55 m. Similar results are seen at the Eltanin. Profile RO257 increases from 1.81 to 2.82 m in going from a 0 to 200 k m exclusion width and on the opposite limb, offsets on profile RO400 increase from 1.95 to 3.66 m. Increasing the exclusion width to 100 k m and 200 km can substantially increase, and in some cases, more than double the amplitude of the estimated geoid offset. An increase in the geoid offset with increasing exclusion width is expected. Detrick [4], and Sandwell and Schubert [5] attributed one source of this increase to horizontal heat conduction across the fracture zone which tends to smooth out the abrupt geoid step. The sloping of the geoid towards the fracture zone biases the estimate of the regional polynomial and causes an underestimate of the offset. Additional anomalies near the fracture zone can also severely bias the regional polynomial estimates (Fig. 2). Almost all profiles across the Udintsev fracture zone display an anomaly adjacent to the fracture zone on the older side which is 150-200 k m wide and 0.5-1.0 m high. Parmentier and H a x b y [14] modeled this anomaly as a displacement caused by bending moment

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stresses at the fracture zone. If the anomaly is included in the least-squares fit, the section of the polynomial on the older side of the fracture zone slopes up towards the offset in order to accommodate the anomaly. This leads to an incorrect estimate of the form of the regional polynomial and to a reduced geoid offset. The effects of both horizontal heat conduction, and anomalies adjacent to the fracture zone can be avoided by using an exclusion width of between 150 and 200 km. There are obviously limitations on the m a x i m u m size of this exclusion width. The total length of the observed profile must be long enough to allow a large exclusion width while still retaining a sufficient number of endpoints to accurately estimate the regional field. On several of the Seasat profiles, the segment of unsable profile between the

Udintsev and Eltanin fracture zones is only 300-400 k m long. In these cases, and in cases where neighboring tectonic features (e.g. other fracture zones, seamounts, etc.) limit the length of the geoid profiles, we have used a smaller exclusion width. The geoid offset can be measured from profiles which contain signals at all wavelengths, or on profiles which have had a reference field removed since a polynomial can approximate the regional field in either case. However, because the long-wavelength geoid and the computed reference field cannot be represented exactly by second-order polynomials, the estimated geoid offsets are affected by the choice of profiles. In order to determine the magnitude of this effect, geoid offsets were estimated from both the full geoid profiles and from profiles with a reference field removed. The G E M 9 reference field with coefficients up to degree and order 10 was subtracted from the profiles which left anomalies having wavelengths less than approximately 4000 km. For each profile across the Udintsev fracture zone, an exclusion width of 150 k m was used. Across the Eltanin, a larger width of 200 k m was used in order to span the closely-spaced Heezen and Tharp fracture zones. The results of this analysis are shown in Fig. 3. On the west limb of the Udintsev, the offsets estimated from profiles which have had the reference field removed are with few exceptions larger than those estimated from the full profiles. For the youngest 12 profiles this difference averages 0.23 m whereas the remaining profiles vary b y less than 0.12 m. On the east limb of the Udintsev the amplitude of the variations between the two sets of measurements are similar but in contrast to the western limb, the estimates from the full geoid profiles are larger than estimates from the profiles with the reference field removed. The differences in the youngest 8 profiles average 0.23 m and the remaining profiles except for the oldest vary by less than 0.14 m. Offset determinations from the two sets of profiles across the western trace of the Eltanin are similar and vary on the average by only 0.07 m. In all cases, measurements from the full geoid profiles are slightly larger. In contrast, differences between the two sets of measurements across the eastern branch of the fracture zone are large. In all

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295 cases measurements from the profiles which have had the reference field removed are up to 0.38 m larger and are on the average 0.25 m larger than those estimated from the full geoid profiles. The variations in geoid estimates obtained from the two sets of profiles are fairly consistent on each branch of the fracture zones but the magnitude of the deviations vary between the branches. On each limb of the fracture zones the deviations show up as a bias rather than as r a n d o m errors. The effect of a variable magnitude bias on the measurements will change the observed trends of the geoid slope versus age curves slightly, but will modify the overall amplitude, and hence, the plate thickness estimates. For these reasons, it is useful to look at geoid slope estimates across each branch of the fracture zones separately in order to avoid scatter that may be caused by the observed biases and not by lithospheric thickness variations. The choice of whether to use profiles with or without a reference field removed, therefore, appears arbitrary. Because the step arising from seafloor age variations is more prominent in profiles which have had a reference field removed and deviations from the estimated polynomial and observed geoid are easier to see, geoid offsets for this paper were computed from profiles with the reference field removed. 4. Results

The locations of Seasat arc segments used in this analysis are shown in Fig. 4. These profiles all show clear geoid offsets at the fracture zones without additional large anomalies elsewhere on the profiles (except within the excluded area near the fracture zone axis). Offsets were determined on each profile using exclusion widths of 0 km, 150 km and 200 km, and the largest exclusion width which gave a reasonable fit to the profiles was used. In m a n y cases both the 150 k m and 200 k m widths gave reasonable values and the average of the two measurements was used as an estimate of the regional offset, and the variation between them as an estimate of the range of possible values. The error estimates in cases where only one exclusion width was chosen were determined visually. This visual estimate was in all cases equal to or larger than the calculated root-mean-square error between the observed and estimated profiles

(calculated using only those segments of the profile used in the least-squares estimation). The calculated error in most cases was less than 10 cm whereas the difference in estimates of the regional offset based on different exclusion widths varied by as much as several tens of centimeters. The location of the profiles and the estimated regional offset and error are listed in Table 2. Results from the Eltanin Fracture Zone System are shown in Fig. 5a and b. Also plotted are theoretical geoid slope-age curves for plate thicknesses of a = 6 0 k m and 90 km, where geoid slopes are derived using the derivative of the long-wavelength isostatic approximation (equation (2)) and are given by: dN(t) dt

4"lrGPmOaCT m ( £ (__l)n+X g

n=a

×exp(-flnut/a ) + 2 w ( t ) × Y'~ exp(-B2~_lut/a)

(4)

n=l

with:

~n= [(R2 + n2qT2)l/2- R], R = ua/2x, and:

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8/~r2~_,l/(2n - 1) 2

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(5)

Values for the thermal parameters used in the calculations are given in Table 1. The theoretical curves are used only as a reference to the expected decrease in geoid slope values for different plate thicknesses and are not intended to represent the best-fitting plate parameters. It is clear that the observed geoid slope values do not follow a curve predicted by a single plate thickness. Instead, on the west side of the Eltanin there appears to be three separate segments that deviate from the theoretical curves; one for average ages less than 18 m.y., a second for ages between 18 and 40 m.y. and third for ages greater than 40 m.y. On the east side of the Eltanin two trends are seen, one for ages less than 40 m.y., and the other for ages greater than 40 m.y. It is useful to identify and compare profiles along critical

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TABLE 2 Profile locations and estimated regional offset and error ELTANIN

WEST

PROF[LE R0832 R0631 R0674 R0430 R0188 R0803 R0602 R0487 R0243 R0530 R0286 R0774 ROB17 R0860 R0659 R0171 R0458 R0214 R0257

LAT. -50.06 -50.12 -50.49 -50.53 -50.56 -51.97 -52.13 -53.02 -53.06 -53.30 -53.33 -53.40 -53.78 -54.07 -54.0B -64.14 -54.39 -54.40 -54.62

ELTANIN

EAST

PROFILE R0515 R0558 R0802 R0601 R0845 R0400 R0588 R01275 R0687 R0730 ROB29 R0773 R0859 R0457 R0543 R0830 R0672 R0428 ROBf4

LAT. -56.30 -56.54 -56.6B -56.77 -57.01 -57,06 -57.13 -57.17 -57.23 -57.44 -57.61 -57.65 -58.25 -58.52 -58.91 -59.34 -69,70 -59.73 -60.41

LONG. 213.07 213.24 214.29 214.42 214.56 218.07 218,46 221.89 222.02 223.00 223.13 223.32 224.90 226.32 226.34 226.61 227.53 227.70 228.85

AGE 64.5 64.3 63.3 63.3 63.0 57,1 55.6 40.2 40.0 36.0 35.6 35.0 31.0 27.5 27.5 26.6 24.5 24.2 21.4

AGE 40.0 38.2 35.6 35.6 34.0 18.0 16.4 4.5 4.3 1.8 1.7 t.t t.4 3.2 3.2 4.0 4,3 4,6 6.5

OFFSET(M) 1.76 1.38 1.53 1.71 1.80 1.t5 1.46 2.98 2.73 3.79 3.88 3.42 4.89 4.16 4.24 4.44 3.18 3.20 2.85

ERROR(M) .35 .15 .20 ,.15 .25 .35 .40 .25 .25 .20 .25 .35 .40 .20 .25 .20 ,15 .20 .20

DN/DT(CM/MY) 7.18 5.29 5.52 6.17 6.21 2.94 3.72 8.35 7,65 1t.08 11.45 10.09 16.52 17.12 17.45 t6,65 15.74 16.33 19.13

ERROR(CM/MY) 1.43 0.57 0.72 0.54 0.86 0,90 t.02 0.70 0.70 0.58 0.74 1.03 1.35 0.82 1.03 0.88 0.74 1.02 1.34

WIDTH E E E E E C C D O D D O E D O D D D D

LONG. 235.19 236.29 236.92 237.37 238.32 238.56 238.94 239,26 239.57 240.83 242.00 242.38 245.2~ 246,46 248.66 250.54 251.6t 251.73 253.41

AGE 5.4 3.0 1.9 1.2 0.5 0.8 1.3 1.6 2.0 3.4 5.3 5.9 11.4 15.0 21.6 27.3 3t.1 31.6 37.8

AGE OFFSET(M) 19.5 -1.76 23.8 -3.02 26.1 -3.50 28.0 -3.48 29,7 -2.89 30. t -3.62 30.8 -2.7B 31.1 -3,12 31.7 -3.33 34.2 -2.28 37.6 -2.t4 38.2 -2.16 45.6 -1.18 49.9 -3,51 57.9 -3.13 60.8 -2.59 62.3 -2.59 62.5 -2.09 65.0 -1.94

ERROR(M) .35 .25 .20 .20 .35 .20 .30 .35 .25 .25 .36 .35 .40 .35 .35 .20 .25 .30 .25

ON/OT(CM/MY) t2.48 14.52 14.46 12.99 9.90 12.35 9.42 10.58 tl.21 7.40 6.63 6.69 3.45 10.06 8.62 7.73 8,30 6.76 7.13

ERROR(CM/MY) 2.48 1.20 0.83 0.75 1.20 0.68 1,02 1.19 0.84 0.8t t.08 1,08 1.17 1,00 0.96 0.60 0,80 0.97 0.g2

WIDTH C C D O D D D D D D C C D C O C O D D

208.94 208.76 208,52 207.74 207,55 206.64 206.02 205.68 204.74 204.63 203.77 203,68 202,77 202,54 201.51 20t.34 2C0.59 2C"0.00 199.79

28.6 29.0 29.9 32.0 32.5 37.7 41.1 42.8 45,3 45.6 48.8 49.4 54.0 55.5 58.3 59.0 60.5 61.0 61.5

1t.3 11.8 t3.0 16.7 18.1 2t.6 23.5 25.0 27.7 28.0 31.6 32,0 36.5 37.8 42.4 43.3 46.7 51.5 62.0

1.68 1.68 1,79 t.60 2.05 2.39 2.73 2.6t 2.75 2.40 2.46 1.91 t.71 t.90 1.82 2.05 t.45 0.80 0.69

LONG. 219.42 220.56 220.60 220,81 221.76 223.10 225.26 227.12 227.43 227,55 227.73 228.73 228.93 229.89 235.96 237.69 238,49 241.92 243.56 244.58 246.07 246.74

AGE 0.5 t.3 1.3 1,7 3.1 5.1 8.1 tl.2 11.5 11.7 12.0 13.3 13.5 15.0 39.5 43.5 46.3 65.8 58.8 60.1 62.5 63.7

AGE 9.4 12.0 12.0 12,6 14.7 17.5 23.4 29.5 30.1 30.3 30.5 32.5 32.8 34,9 54.0 57.8 59.2 63.3 65.9 67.4 70.5 71.7

OFFSET(M) -t.68 -t.66 -t.35 -t.39 -t.45 -t.39 -1.30 -t.64 -t.88 -2.04 -1.86 -0.99 -1.45 -t.3t -0.64 -1.14 -0.76 -0.49 -0.76 -0.72 -0,42 -0.45

U O I N T S E V WEST

R0430 R0674

R 0875 R0631 R0832 R0588 R0789 R0545 R0258 R0502 R0216 R0459 R0172 ROB61 R0617 R0815 R0574 R0775 R0287 UOINTSEV PROFILE ROB17 ROB6O R0659 R017t R0459 R0257 R0587 R0874 R0673 R0429 R0185 R0716 R0223 R0515 R0773 R0615 ROB59 ROB43 ROB30 R0672 R0514 R0557

-53.96 -53.97 -53.86 -53.60 -53.54 -53.28 -53.12 -52.82 -52.50 -52,44 -52.04 -52.06 -51.6t -51.49 -61.08 -50.86 -50.53 -50.11 -50.0t

.35 .35 .25 .20 .15 .15 .t5 .30 .30 .30 .20 .20 ,20 .25 .20 .20 .20 .20 .15 .25

8.84 9.71 9.77 10.59 10.46 14.24 14.84 16.51 14.66 15.62 13.64 14.30 t0.98 9.77 10.73 11.45 t3.06 t0.51 8.42 7.26

2,02 2.02 1.45 1.1B 0.98 1.04 0.93 1,70 1.69 1.70 1.t4 1.16 t.15 1.43 1.t3 1.26 1.27 1.45 1.58 2.63

O D D D D O E E E E E E E 0 O D D D O D

EAST LAT. -57.15 -57,52 -57.51 -57.60 -57.B2 -58.02 -58.41 -58.87 -58,89 -58.91 -58.92 -59.03 -59.07 -59.28 -61,18 -61,63 -81.90 -62.47 -82.93 -63.27 -63.97 -64.29

ERROR(M) .20 .25 .25 .20 .20 ,30 .30 .20 .15 .20 .20 .20 .t5 .10 .20 .20 .15 .20 .15 .t5 ,15 .15

ON/DT(CM/MY) 18.88 14.49 t2.62 12.75 12.50 1t.21 8.50 8.96 10.11 10.97 10,05 5.t6 7.51 6.58 4.41 7.97 5.89 6.53 t0.70 9.86 5.25 5,62

ERROR(CM/MY) 2,25 2.34 2.34 1.83 1.72 2.42 1.96 1.09 0.61 1,08 1.08 t.04 0.76 0.50 1,38 1.40 1.16 2.67 2.ti 2.06 1.87 1.87

EXCLUSION WIDTHS: A = 5 0 KM, B = I C ~ KM, C = 1 5 0 KM, D = 2 0 0 KM. E = AVERAGE OF 1 5 0 & 2CK) KM FOR E X C L U S I O N W I D T H S A - O , ERRORS ARE E S T I M A T E D V I S U A L L Y FOR E X C L U S I O N W I D T H E, ERROR I S HALF THE D I F F E R E N C E BETWEEN THE MAXIMUM AND M I N I M U M O F F S E T S O B T A I N E O U S I N G E X C L U S I O N WIOTHS OF 1 5 0 AND 2(]0 KM

WIDTH A A A A A D O O E E E E E E D D D C D 6 B B

298 8

ELTANIN WEST

t+ ~o

A = 90 KM • INACTIVE

~

~

R

0

8

0

3

o WITBIN ACTIVE TRANSFORM

oo

A = 60

d 0,00

10.00

20.00

30.00 40.00 AGE (MY)

50.00

60.00

KM

70,00

b

ELTANIN EAST o

o

0457 R0543

g •

INACTIVE

0859

° o

A = 60

d 0.00

Y0.00

20.00

40.00

30.00

50.00

60.00

KM

70.00

AGE (MY)

Fig. 5. Oeoid slope estimates across the Eltanin fracture zone system and theoretical geoid slopes calculated from a thermal plate cooling model with plate thicknesses of 60 km and 90 kin: (a) across the western limb of the fracture zone; (b) across the eastern limb.

segments of the fracture zone to see if the variations in the geoid s l o p e - a g e plots are real or possibly caused b y problems in the measurement

technique. T o do this c o m p a r i s o n we have identified several profiles along key sections o f the curves. These are plotted together with their least-

299 squares estimates of the regional geoid and the theoretical geoid based on a chosen plate thickness and the ages of the lithosphere across the fracture zone. The geoid profile across a fracture zone can be determined from a given temperature distribution and the long-wavelength, isostatic approximation to the geoid (equation (2)). Using the temperature structure appropriate for the platecooling model and placing the fracture zone at x = 0, the geoid anomaly is given by:

with:

4GPrnaTma2~

#(t) =

gqT × exp(. -

( - 1 ) "+1

n=l

//2

n2~2Kta2)

where t o is the age offset of the fracture zone and t is the age of the younger seafloor. The functions are the geoid relations far from the fracture zone and are one-dimensional approximations to the full series solutions. At plate

O(t)and O(t+ to)

velocities appropriate to the Pacific-Antarctic Ridge there is little difference between the approximate and the full expressions. To compare the thermal plate estimate with the observed profile, the regional geoid calculated in the leastsquares fitting routine is subtracted from the observed profile. In the figures where the theoretical and observed profiles are compared, the vertical position of the theoretical profile was adjusted so that the mean values of the geoid heights outside of the exclusion zone on both the observed and theoretical profiles coincided. On the western side of the Eltanin, profiles RO817 and RO774 (Fig. 5a) are located only 110 krn apart but fall on different parts of the geoid slope-age curves. Profile RO817 lies more closely to the curve for a 110-120 k m thick thermal plate, whereas profile RO774 is more compatible with a 60-70 k m thick plate. On comparing the estimated geoid offset and predicted geoid profiles based on the plate model with the observed geoid profiles (Fig. 6a, b) it can be seen that the estimates of the regional geoid offset are reasonable and that the thermal plate thicknesses which can be used to fit these two profiles differ by 50-60 kin. It is interesting to note that profile RO774 is located slightly west of the active ridge crest segment between the Udintsev and Tharp fracture

b

~05.0]

~ 5.0t

~'2 1

--=2.5

i.

S

a;o

4;0kilometers sbo

a;o

=ooo N

O.

Eltanin

.................... S

2oo

4oo

soo

~o

a=70km a =120km

qo~o N

kilometers

Fig. 6. Geoid profiles across the Eltanin fracture zone system. (a) Geoid profiles with GEM9 reference field removed (l = m = 10), and estimated regional polynomial and offset. A 200 km exclusion width is used. (b) Geoid profiles with the estimated regional polynomial removed, and theoretical geoid profiles for plate thicknesses of 120 km and 70 kin.

300

R0803 R0805

R0~86 " H

5i]

50

R0186

~

~ 2.5 E H O.

S

2;o

4;o kilometers

~;o

80o

N

S

a:6Okm a=90km

2oo

~& kilometers

6oo

eoo N

Fig. 7. Geoid profiles across the Eltanin fracture zone system. (a) Geoid profiles with GEM9 reference field removed (l = m = 10), and estimated regional polynomial and offset. A 200 km exclusion width is used. T refers to the location of Tharp fracture zone, H to location of Heezen fracture zone. (b) Geoid profiles with the estimated regional polynomial removed, and theoretical geoid profiles for plate thicknesses of 60 km and 90 km.

zones, and profile RO817 is slightly east of the ridge segment and crosses the active transform region. Within the active transform, the equation for geoid heights (equation (6)) is not strictly valid. The initial conditions are set at the r i d g e - t r a n s f o r m intersection and the lithosphere is assumed to be cooling at all other times. This criterion is not met within the transform zone. Far from the fracture zone, however, geoid heights calculated using equation (6) are valid. Another two profiles which constrain the overall trends in the data are profiles RO803 and RO186 (Fig. 5a) which are separated by 290 km. Profile RO803 lies at the older end of the segment of the geoid slope-age curve that is most compatible with the curve for a plate thickness of 60 k m and profile RO186 is at the y o u n g end of the curve best-fit by a 90 km thick plate. The observed profiles and their least-squares estimates of the regional geoid and offset are shown in Fig. 7a. As before, the observed minus the regional geoid, and the theoretical profiles for plate thicknesses of 60 and 90 k m are shown in Fig. 7b. Again, the least-squares estimates of the regional offset appear to be reasonable. Profile RO803 is very closely matched by the theoretical profile for a plate thickness of 60 km whereas profile RO186 is

better fit by a profile calculated using a larger plate thickness of 90 km. Finally, profiles RO859, RO457, and RO543 f r o m the east side of the Eltanin are examined in the same manner. Profiles RO859 and RO457 are separated by only 80 km. The observed and calculated curves are shown in Fig. 8 for plate thicknesses of 55 and 90 km. It is clear that profile RO859 displays an offset most compatible with a fairly thin plate thickness between 55 and 60 km. Profiles RO457 and R O 543 on the other hand, are better m a t c h e d by a larger plate thickness of a r o u n d 90 km. The large deviations in the estimated geoid slopes for profiles located very near each other on the Eltanin fracture zone system appear to be real and not a result of errors in the measurement technique. The geoid s l o p e - a g e relationship on both sides of the fracture zone is similar although not identical (Fig. 5a, b), with major differences occurring primarily at ages less than 15 m.y. The geoid s l o p e - a g e relationship is not as consistent across the two sides of the Udintsev fracture zone as it is across the Eltanin (Fig. 9a, b). On the west side of the Udintsev, geoid profiles with average ages of less than 17 m.y. contain large anomalies near the fracture zone on the

301

J ........................ /

j,"-. . . . . . . . . . . . . . .

.

50

..........

50t Ro5,3 2.5" ~

O.i S

I 200

i 400

i 600

I 800

J Iooo

N

kilometers

O. S

~ 200

.

.

.

.

.

.

.

.

.

.

.

.

a = 90

km

.................................. 55 l 400

'

l

600

8;0

i000 N

kilometers

Fig. 8. Geoid profiles across the Eltanin fracture zone system. (a) Geoid profiles with GEM9 reference field removed (1 = m = 10), and estimated regional polynomial and offset. A 200 km exclusion width is used. (b) Geoid profiles with the estimated regional polynomial removed, and theoretical geoid profiles for plate thicknesses of 55 km and 90 kin.

older seafloor, and the geoid offset also increases very gradually towards the younger side although for these young seafloor ages an abrupt increase would be expected. Geoid offset estimates from these profiles show no systematic increase as the exclusion width is increased and on most profiles the offset determinations change erratically as the exclusion width is varied. These profiles were not considered to be reliable and were not included in the geoid slope analysis. Between 20 and 35 m.y. an increase in the geoid slope values with age is apparent. For ages greater than 35 m.y., the geoid slope estimates decrease gradually, consistent with a plate thickness of 100-120 km. The unexpected increase in geoid slopes for average ages between 20 and 35 m.y. on the west side appears to be real and not a result of errors in the estimation technique. Fig. 10 shows the five profiles between 20 and 25 m.y. along with estimated regional offsets determined using exclusion widths of 100 and 200 km. Although the younger, southern side of the profiles are adequately determined by the estimated polynomials, the regional field on the northern side is difficult to estimate because of the large anomaly adjacent to

the fracture zone. The anomaly is up to 200 km wide and 1 m high. As before, the regional field has been removed and the offset compared with those predicted for theoretical plate thicknesses of 60 and 90 km. The 3 younger profiles, RO186, RO430 and RO674, are more closely fit by a theoretical plate thickness less than 90 km. The older profiles, RO275 and RO631, however, are better fit by a 90 k m thick plate. On the east side of the Udintsev there is a gap in the data between average ages of 30 and 45 m.y. (Fig. 9b). Profiles within this region contain large anomalies on the older side of the Udintsev with amplitudes of approximately 1.0 m and widths up to 200 km. In addition, the northern baseline is extremely short because of a similar anomaly on the older side of the Eltanin. For ages younger than 30 m.y. the geoid slope estimates follow the trend defined by a plate thickness between 50 and 70 km. For ages greater than 45 m.y. the scatter is large and it is difficult to ascertain the overall trend of the geoid slope values. For example, if the older two measurements were removed, geoid slope values would appear to increase with increasing age, contrary to what is theoretically ex-

302 a

UDINTSEV WEST

o~

+ttt+,

t+

KM

A = 6 0 KM 0 00

10.00

20 00

3000

40.00

50.00

60.00

40.00

sooo

6o00

70.00

AGE (MY)

UOINTSEV EAST o

g

~o 0.00

A = 6 0 KM 1'000

2ooo

3ooo

70.00

AGE (MY)

Fig. 9. Geoid slope estimates across the Udintsev fracture zone and theoretical geoid slopes calculated from a thermal plate-cooling model with plate thicknesses of 60 km and 90 km: (a) across the western limb of the fracture zone; (b) across the eastern limb.

pected. Conversely, if we disregard the two largest geoid estimates, then a decrease in geoid slopes would be perceived. U n f o r t u n a t e l y , with the data available, little can be said a b o u t the general t r e n d

of geoid slope values at these older ages, although the c o n t i n u e d presence of a geoid offset in the profiles strongly suggests that a thermal a n o m a l y persists across the fracture zone. F o r this to be

303

~0186

R0186

R

R0430

R0674

R0674

R0875

R0631 75.

75

5.0.

50"

Ro65t

¢ ~ ¢~"-------

---- --- a = 60 km e = 9 0 km

2.5-

25"

f Udintsev

Udintsev

z60

4bo

6;0

e;o

,doo

E260 N

kilometers

200

400

600

800

I000

1200

N

kilometers

Fig. 10. Geoid profiles across the Udintsev fracture zone. (a) Geoid profiles with GEM9 reference field removed (l = m = 10), and estimated regional polynomial and offsets determined using exclusion widths of 100 km and 200 km. (b) Geoid profiles with the estimated regional polynomials removed compared to theoretical geoid profiles calculated for plate thicknesses of 60 km and 90 km.

true the plate thickness must be larger than 60 km. Geoid slope values for average ages greater than 50 m.y. all lie near or above the theoretical curve defining geoid slopes for a 90 k m thick plate. In summary, we find that across the east and west limbs of the Eltanin and across the east limb of the Udintsev, geoid slope estimates decrease rapidly for ages less than 35 m.y. and then increase over a relatively short time and distance interval. This is followed by a less rapid decrease as the age of the seafloor increases. The geoid slope versus age plot for the western limb of the Udintsev differs from the other plots and shows an increase in geoid slope estimates for ages between 20 and 35 m.y. followed by a gradual decrease for increasing average ages. N o r t h of the

western limb of the Udintsev fracture zone, the Eltanin fracture zone system is replaced by the Louisville Ridge which is c o m p o s e d of discrete seamounts and ridges aligned along a trend similar to that of the Eltanin fracture zone system [15]. A l t h o u g h we have not crossed the summits of any seamounts "with the n o r t h e r n baselines of our analyzed profiles, they m a y still affect the regional geoid offset because the excess mass of the s e a m o u n t deflects the oceanic lithosphere and creates a surrounding moat. Both the flexed lithosphere and the excess mass of the seamount contribute to the regional geoid, the magnitude and wavelength of the effect depending on the size and c o m p e n s a t i o n of the seamount. Because of this variability, it is not simple to predict the effects of

304 the Louisville Ridge on estimates of the regional geoid offsets, but it is likely that they are affected to some extent. 5. Discussion

The geoid slope measurements across the Udintsev fracture zone and the Eltanin fracture zone system are not consistent with the thermal plate cooling model. Segments of the observed geoid slope versus average age curves from the Eltanin closely follow theoretical curves for a 60 km plate-cooling model (10-35 m.y.) and a 90 km thick plate (35-60 m.y.) although a single plate thickness cannot account for the entire set of measurements. Similar results have been found in the South Atlantic across the Ascension fracture zone where geoid slopes also show two distinct trends [16,17]. For ages less than 30 m.y., the geoid slopes decrease rapidly, consistent with a thin, 50-75 km thermal plate. At older ages, they rapidly increase in magnitude and then decrease more slowly, consistent with a thicker plate (75-100 km), Any proposed cooling model must satisfy both the geoid slope and seafloor depth observations. In the South Pacific the mean depth versus age curve for seafloor ages less than 80 m.y. is proportional to the square root of age and can be approximated by the empirical formula [2]:

w(t) =

2681 + 337~/t-

(t i n m . y . )

(7)

At ages greater than 80 m.y. the depth versus age curve flattens out, consistent with a finite plate thickness [9]. The minimum plate thickness necessary to match the observed depths out to 80 m.y. would be 120 kin. At 80 m.y. the depth predicted by a 120 km thick plate is shallower than the empirical curve by - 2 0 0 m which is within the scatter in the data. Plate thicknesses less than this will predict even shallower depths. A 60 km thick plate for seafloor ages less than 35 m.y. (as derived from the geoid slope estimates), therefore, cannot accurately predict seafloor depths for these ages. Comparing depths from the plate-cooling model to the empirical depth curve (from equation (7)) shows that by 35 m.y., the plate model predicts depths up to 370 m shallower than the empirical depth curve (Fig. 11). If a plate thickness of around 90 km is postulated for older

seafloor, again based on the geoid slope curves, the deviations between the predicted curve based on the plate model and the observed seafloor depths become increasingly larger with age. Comparing these results with the depth anomaly map for the South Pacific [2] does not reveal a progressive increase in the depth anomalies with distance from the ridge crest. A + 600 m anomaly is seen over the western limb of the Eltanin, corresponding to the Louisville Ridge, but except for isolated +400 m depth anomalies near 9 0 ° W , 60°S, the eastern limb has only minor depth anomalies on the order of 0-200 m. Seafloor depths, then, do not support the existence of a thin plate (60-90 kin) as an explanation for the observed geoid slope versus age relationship. Seafloor depths north of the Eltanin subside at a slightly faster rate than depths south of the fracture zone [2,9]. Geoid heights have also been observed to decrease at different rates north and south of the Eltanin [18] although these observations are difficult to interpret in the presence of long-wavelength anomalies and are thus less reliable evidence of a change in effective thermal plate thickness across the fracture zone. It, however, these differences in subsidence rate and geoid slopes are caused by such a change then the expected form of the geoid slope versus age relationship measured across the Eltanin would also change. We can look at possible behaviours of the geoid offset by assuming a very simplistic model in which lithosphere north of the Eltanin is characterized by a 120 km thick thermal plate and by a 100 km plate south of the fracture zone. The initial height of the geoid at both ridges is assumed to be identical which generally will not be the case in the presence of long-wavelength noise (signals unrelated to conductive cooling). With these assumptions, the calculated geoid heights and geoid slopes are shown in Fig. 121 and b. The geoid slope versus age relationship differs across the two limbs of the fracture zone and for different values of the age offset. Assuming a rightlateral offset, geoid slopes decrease quickly across the eastern limb of the fracture zone, then change sign at large enough ages. This occurs when geoid heights on the thinner plate reach their equilibrium value and the geoid heights associated with the thicker plate continue to decrease below this value. In contrast, geoid slopes across the

305

5 9

o

A = 6 0 KM

A = 9 0 KM o

EMPIRICAL CURVE

d to

000

1000

2000

3000 AGE

40.00

5000

6000

IMY)

Fig. 11. Depth curves calculated from the thermal plate-cooling model assuming plate thicknesses of 60 km and 90 km, and the empirical depth curve for the South Pacific determined by Schroeder [2].

western limb of the fracture zone initially decrease and then increase until reaching a constant value. At large enough ages the geoid heights across each limb of the fracture zone reach constant values and geoid slopes then remain constant through time. Although at large ages the magnitude of the geoid slopes will be the same across both limbs of the fracture zone, their signs will be opposite. These predicted geoid slopes are not observed across the Eltanin (Fig. 5a, b) where both limbs of the fracture zone display trends which are remarkably similar. Deviations from the theoretical geoid slopes that are observed in the measurements across the Eltanin cannot be explained by a sudden discontinuity in plate thickness across the fracture zone. The model used in this comparison is extremely simplified, however, and changes in effective plate thickness across the Eltanin cannot be completely discounted. An important contribution to the observed geoid anomalies which we have not considered in our analysis may come from small-scale convec-

tion. Such convection occurs beneath the rigid, cooling lithosphere on scales much smaller than the dimensions of the oceanic plates. Numerical experiments on the onset time and development of small-scale convection beneath cooling oceanic lithosphere [19,20] do not predict rapid changes in the geoid slope-age relationship and cannot explain the relatively rapid changes in geoid slope we observe on profiles separated by less than a few hundred kilometers. The type of convection modeled above is instigated by small instabilities in the temperature structure of the cooling lithosphere. At a fracture zone, however, a large, horizontal gradient exists between the older, thicker and cooler lithosphere and the younger, hotter lithosphere. This horizontal gradient drives a flow that eventually develops into a cold downwelling plume beneath the older lithosphere and an upwelling plume beneath the younger portion [21,22]. Shear coupling then causes a series of convecting cells to develop to the sides of the circulation beneath the fracture zone. The normal stresses

306

AGE(MY)ONNORTHSIDE 30 00

20 00 i .....

RIO

) 0 O0 i

0 00 i

1000 i

20 00 t

30.00 i

40 00 ~

5000 J

6000

G

I/d

KM

0 00

I 0 00

20 00

3000

40.00

50 00

60.00

7000

80.00

9000

AGE(MY#ONSOUTHSIDE

b

8

~E

~ oo td

0 MYlEAST)

DT = 20 MY(EAST)

oo td 10.00

~'ooo

3oo0

,,o.oo

~'o.oo

~ooo

~o.oo

~o.oo

~o.oo

,oo.oo

AVERAOEAGE (MY) Fig. 12. (a) Theoretical geoid height values for plate thicknesses of 100 and 120 km. (b) Oeoid slope estimates across a fracture zone assuming a 120 km thick plate north of the fracture zone and a 100 k m thick plate to the south. Geoid slope estimates for offsets of 20 m.y. and 30 m.y. are shown.

and temperature anomalies arising from the convection will produce short-wavelength geoid and depth anomalies at the fracture zone. Although it is not clear how convection at a fracture zone will affect the d e p t h - a g e or g e o i d - a g e relations, the

presence of the anomalies will significantly change the measured geoid offset at the fracture zone when the offsets are measured with the same m e t h o d as used in this paper [22]. R o b i n s o n et al. [22] have shown that after the development of

307 convection there are relatively r a p i d changes i n the estimated geoid offsets. The m a g n i t u d e of these changes a n d the estimated geoid slope versus age curves vary with changes i n the p a r a m e t e r s of the convection models (e.g., viscosity structure, Rayleigh n u m b e r , etc.). These results suggest that although the m e t h o d used in this p a p e r to estimate geoid offsets avoids anomalies within several h u n d r e d kilometers of the fracture zone, the measured geoid offsets m a y still be c o n t a m i n a t e d b y anomalies u n r e l a t e d to the m e a n , regional geoid offset. A t this point, a d d i t i o n a l studies o n the geoid slope versus age relationship are necessary i n order to determine the exact form of this relationship. A t fracture zones, anomalies caused by flexure, b e n d i n g stresses, a n d possibly small-scale convection, a n d the limited length of the geoid profiles to each side of the fracture zones m a k e it difficult to accurately determine the regional geoid offset. Likewise, we have already n o t e d that m e a s u r i n g geoid heights directly as a f u n c t i o n of age is extremely difficult because of the presence of large-amplitude anomalies which are u n r e l a t e d to the cooling of the lithosphere. I n conclusion we have d e t e r m i n e d the geoid slope versus age relationship across the E l t a n i n a n d U d i n t s e v fracture zones a n d have f o u n d consistent relationships across three of the four fracture zone limbs. O u r results suggest that although the simple plate cooling m o d e l accurately predicts seafloor depths to ages at least as old as 80 m.y. B.P., the m o r e sensitive geoid a n o m a l i e s reveal i n a d e q u a c i e s in the predictive ability of the cooling model. A d d i t i o n a l , u n m o d e l e d effects such as small-scale convection m a y be affecting the observed geoid offsets.

Acknowledgements M a n y t h a n k s to E.M. R o b i n s o n for reviewing a n early draft of this m a n u s c r i p t a n d A.P. Freedm a n for help in c o m p u t e r p r o g r a m development. This research was supported b y O N R c o n t r a c t N00014-86-k-0325 to M . I . T . M . L . Driscoll gratefully acknowledges the s u p p o r t provided b y the M.I.T. D e p a r t m e n t of Earth, Atmospheric, a n d P l a n e t a r y Sciences d u r i n g part of 1986.

References I B. Parsons and J.G. Sclater, An analysis of the variation of ocean floor bathymetry and heat flow with age, J. Geophys. Res. 82, 803-827, 1977.

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